Subtracting Fractions — the 80/20
Make denominators match (LCD), subtract numerators, simplify. Borrow when using mixed numbers. The calculator shows each step.
How it works
- Find the least common denominator.
- Rewrite each fraction with the LCD.
- Subtract numerators; keep the common denominator.
- Simplify; convert to mixed number if improper.
Sanity checks
- Same denominators → only numerators change.
- 5/6 − 1/4 → LCD 12 → 10/12 − 3/12 = 7/12.
- Subtracting a larger fraction should yield a negative result.
Shortcuts
- Same denominator: subtract numerators directly.
- If one denominator divides the other, use the larger as LCD.
- Mixed numbers: convert to improper to avoid borrowing errors.
Pitfalls
- Subtracting denominators (wrong).
- Forgetting to borrow when needed with mixed numbers.
- Dropping the negative sign in the result.
Micro‑examples
- 7/9 − 2/9 = 5/9.
- 3 1/4 − 1 2/3 → 13/4 − 5/3 = 39/12 − 20/12 = 19/12 = 1 7/12.
- 1/4 − 3/4 = −1/2.
Mini‑FAQ
- Do I need LCD? Any common denominator works; LCD keeps numbers small.
- Negative fractions supported? Yes—rules are the same.
- Mixed results? Convert to mixed number for readability.
Action tip
Enter two fractions or mixed numbers; the tool finds the LCD, subtracts, simplifies, and shows a mixed number if needed.